Related papers: Acceleration of complex matrix multiplication usin…
We dispel with "street wisdom" regarding the practical implementation of Strassen's algorithm for matrix-matrix multiplication (DGEMM). Conventional wisdom: it is only practical for very large matrices. Our implementation is practical for…
Let {\alpha} be the maximal value such that the product of an n x n^{\alpha} matrix by an n^{\alpha} x n matrix can be computed with n^{2+o(1)} arithmetic operations. In this paper we show that \alpha>0.30298, which improves the previous…
As the most central and computationally intensive component of deep neural networks, the execution efficiency of matrix multiplication directly determines the training and inference performance of models. Harnessing the parallel processing…
We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…
Matrix multiplication $A^t A$ appears as intermediate operation during the solution of a wide set of problems. In this paper, we propose a new cache-oblivious algorithm for the $A^t A$ multiplication. Our algorithm, A$\scriptstyle…
Parallel matrix multiplication is one of the most studied fundamental problems in distributed and high performance computing. We obtain a new parallel algorithm that is based on Strassen's fast matrix multiplication and minimizes…
In this paper, we propose a method for emulating double-precision general matrix--matrix multiplication (DGEMM), a fundamental and performance-critical kernel in many high-performance computing applications. Ozaki-I and Ozaki-II are…
We present a novel approach for accelerating convolutions during inference for CPU-based architectures. The most common method of computation involves packing the image into the columns of a matrix (im2col) and performing general matrix…
On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and…
The classic method for computing the spectral decomposition of a real symmetric matrix, the Jacobi algorithm, can be accelerated by using mixed precision arithmetic. The Jacobi algorithm is aiming to reduce the off-diagonal entries…
This article presents a new method to compute matrices from numerical simulations based on the ideas of sparse sampling and compressed sensing. The method is useful for problems where the determination of the entries of a matrix constitutes…
Matrix multiplication is a foundational operation in scientific computing and machine learning, yet its computational complexity makes it a significant bottleneck for large-scale applications. The shift to parallel architectures, primarily…
Matrix multiplication is the bedrock in Deep Learning inference application. When it comes to hardware acceleration on edge computing devices, matrix multiplication often takes up a great majority of the time. To achieve better performance…
General Matrix Multiplication (GEMM) is a critical operation underpinning a wide range of applications in high-performance computing (HPC) and artificial intelligence (AI). The emergence of hardware optimized for low-precision arithmetic…
We show that the product of an nx3 matrix and a 3x3 matrix over a commutative ring can be computed using 6n+3 multiplications. For two 3x3 matrices this gives us an algorithm using 21 multiplications. This is an improvement with respect to…
Large-scale floating-point matrix multiplication is a fundamental kernel in many scientific and engineering applications. Most existing work only focus on accelerating matrix multiplication on FPGA by adopting a linear systolic array. This…
We propose a non-commutative algorithm for multiplying 2x2 matrices using 7 coefficient products. This algorithm reaches simultaneously a better accuracy in practice compared to previously known such fast algorithms, and a time complexity…
Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we…
While there are numerous linear algebra teaching tools, they tend to be focused on the basics, and not handle the more advanced aspects. This project aims to fill that gap, focusing specifically on methods like Strassen's fast matrix…
In recent years, randomized methods for numerical linear algebra have received growing interest as a general approach to large-scale problems. Typically, the essential ingredient of these methods is some form of randomized dimension…